i dont really know rhodes, but i know zakynthos quite well. as a whole i would say that zakynthos is a very friendly and beautiful island. but it has been somewhat overun by tourism so you have to know where to go if you want to stay in a nice and quiet place and have any sort of experience of greece.
do not listen to anyone who says laganas is the place to go, especially if you want somewhere quiet. it is a hideous, huge, loud resort that is full of pissed teenagers and it has absolutely nothing to do with greece at all. it is cheap, but that is the onlt thing it has got going for it (unless you are looking for a party holiday where the only important things are getting pissed and having sex!!)
the nicer places to stay on zakynthos are alikanas - but make sure you are staying down near the beach. the area around the crossroads on the road to alikes is wrongly labelled as 'alikanas' but is a bit oif a soulless area really. also nice is the tiny resort of Agios Nikolaos (the one near Argassi on the eastern peninsula NOT the one in the north which is horrid. Porto koukla, near laganas is also ok.
there are also nice pockets of quiet accommodation along the northern coast of zakynthos in the region between tsilivi and alikanas with quiet, pretty little beaches. you might need a car if you are staying there though.
friends of zakynthos have a very good website with lots of info about the island so you can see pics of the resorts and read the reviews there.
just type friends of zakynthos into google.